CLUSTER ANALYSIS OF LANDSAT TM DATA
Masatoshi Mori and Keinosuke Gotoh t
Department of Management Engineering, Kinki University, Iizuka 820, Japan
tDepartment of Civil Engineering, Nagasaki University, Nagasaki 852, Japan
PURPOSE:
Cluster analysis ~ystem by using Statistical Analysis System (SAS) is constructed. The analysis system is applied to Landsat
TM data. The s:x spectral bands except t~e thermal band of TM data are used for analysis. Three hierarchical algorithms
of cluster analysIs, \\:,ard method, a,:,erag~ lmkage, and centroid method, are prepared in the framework of SAS cluster. The
results by three alg;of1thm~ are exammed m relation to classification. The classified map by Ward method is the most accurate
among them, and IS practIcal. On the other hand, the others are almost same and incorrect.
KEYWORDS: Cluster analysis, Image processing, Landsat TM data, SAS
1. INTRODUCTION
as the sea, rivers, ponds, residential, commercial, bare soil,
roads, grass, etc. These typical categories are very important for checking cluster algorithms. We adopted six spectral bands except the thermal (the 6th) band for the analysis system, because the spacial resolution of the thermal
band is 120m, which is different from that of the others,
so we excluded the thermal band. Then we construct the
six-dimensional feature space of TM data.
In use of Landsat Thematic Mapper (TM) Data, cluster
analysis as an unsupervised classification scheme is one of
the most useful methods. Specially, in the case of being
not clear of text area in objective image, cluster analysis
is effective and powerful (Koontz, 1976). A difficulty in
using of cluster analysis is, however, existing in extending
spectral band capacity. There are seven spectral bands in
Landsat TM sensors. Each of these sensors has a dynamic
range with 256 levels (8 bits) nominally. In the first stage
of cluster analysis we construct a multi-dimensional feature
space (Goldberg, 1978). If using all the seven spectral data
of TM in analysis, a seven-dimensional feature space is necessary, which needs 256 7 bits of computer memory (Wharton, 1983). It is, however, impossible to construct this feature space in actuality. Then, as conventional method of
clustering, preprocess of sampling has been adopted. In
this method, before analyzing data, several", several hundred points are selected from original image data. Then,
these selected points are directly analyzed by using clustering scheme, and classified to land cover map. Finally every
point of original data is assigned to the nearest classified
point. As every point of original data is not analyzed directly by this procedure, incorrect classification in assigning
points to the resultant class may occur. The reason is that
the Euclid metric, not isotropic, is used in assigning, category area is not always an ellipsoid in the multi-dimensional
feature space, so erroneous assigning may occur still.
2.2 SAS/cluster procedure
The three algorithms of SAS/cluster procedures are prepared and compared with one another, which- are Ward
method, average linkage, and centroid method. They are
all hierarchical methods. The jobs of clustering are carried
out on IBM 3081 computer and FACOM M-1S00 computer
systems. The CPU time of SAS/cluster procedure is about
11 minutes for three algorithms, but the jobs need more
than 9 mega bytes in computer memory.
(a) Ward method
By Ward method clusters are joined so as to maximize the
likelihood at each level of the hierarchy. Ward method tends
to join clusters with a small munber of observation and is
strongly biased toward producing clusters with roughly the
same number of observations.
(b) average linkage
In average linkage the distance between two clusters is the
average distance between pairs of observations, one on each
cluster. Average linkage tends to join clusters with small
variances and is slightly biased toward producing clusters
with the same variance.
In the present paper we consider a direct analysis of every
point of original data of Landsat TM, without preprocessing for sampling. We use Statistical AnaJysis System (SAS)
(J oyner, 1985) so as to complete this analysis system. By
using SAS system, we can process binary data of multidimensional image. However, as the direct result from SAS
is a set of records, it is difficult to reform the record format
to binary data of classified image. Moreover, because of
direct analysis system, a number of pixels of original image
are limited. We try to examine three algorithms of cluster analysis, Ward method, average linkage, and centroid
method, compared with resultant classified image. The result using TM data is shown precisely.
(c) centroid method
In centroid method the distance between two clusters is defined as Euclidean distance between their centroid or means.
The centroid method is more robust to outliers than most
other hierarchical methods but in other aspects may not
perform as well as Ward method and average linkage.
2.3 Reconstruction to image data
2. CLUSTER ANALYSIS SYSTEM
For direct analysis of image data by SAS, the six image
files of TM data are allocated to device names, respectively.
After the process of clustering procedure, the sample results
by Ward method as shown in Table I are obtained. In the
case of Table I, initially it starts with 1000 pixels, which
are equal to 1000 clusters. Each record of the result means
the one process of joining two clusters to one. In the right
column the frequency means a number of pixels belonging
to a new cluster. Finally one cluster is obtained as known
2.1 Image data
In the present study, we used Landsat-4 TM data (the
scene: 113-37, obtained on May 22, 1984). The square
image of 120 x 120 pixels was cutoff from the scene, which
is shown in Fig.!. This image is a part of Fukuoka City
in Japan, and contains several typical features of land such
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Table I. A sample of the result of SAS cluster procedure by
Ward method.
Number of
clusters
Cluster
Jomted
Frequency of
new cluster
CL48
CL45
CL34
CL23
CL36
CL25
CL39
CL24
CL20
CL28
CL16
CL18
CL27
CL15
CL13
CL7
CL9
CL8
CL6
CLll
CL2
CL58
CL37
CL33
CL46
CL30
CL41
CL26
CL54
CL31
CL29
CL19
CL17
CL21
CL35
CL22
CLIO
CL12
CL14
CL4
CL5
CL3
55
50
189
64
48
377
25
10
73
102
566
112
90
35
85
197
192
45
242
758
1000
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Fig.I. Color composite image of Landsat TM ( the
scene: 113-37, obtained on May 22, 1984).
in Table I.
Then, we can obtain an expected number of clusters by cluster procedure. In the present study we examined the case
of eight clusters for three algorithms. In order to reconstruct classified image from these records, we must know
which one among eight clusters esch pixel of image data
belongs to. Analysis of this tree network gives the relation
between pixels and cluster numbers. Thus we can obtain a
final classified image. This reconstruction process is coded
in FORTRAN77.
The land cover map by centroid method is shown in Fig.2
(c). The result is almost same as- that by average linkage. The main cluster contains almost all-categories in land,
which is more remarkable than the case by average linkage.
4. CONCLUSION
3. RESULTS OF CLASSIFICATION
The cluster analysis system by using SAS has been constructed, and was applied. to Landsat TM data. Three algorithms of cluster analysis, Ward method, average linkage,
and centroid method, were examined and compared with
one another. The classification result by Ward method is
most accurate among them. The results by average linkage
and centroid method are almost same, but average linkage
is somewhat better. However, the separation between water region and land area is rather accurate in classifications
by three algorithms naturally.
3.1 Classification land cover map
Results of classification by three algorithms are shown in
Fig.2 (a)"" (c), respectively. Also the rates of categories are
shown. These map were obtained by reconstruction procedure described in Section 2. Each color used in maps is
assigned to the most suitable category. The field survay has
been performed for checking accuracy of classification.
3.2 Ward method
Although we can analyze six-dimensional image data at one
procedure, the image size is limited to around 120x 120 pixels due to the framework of SAS/cluster. This size is, however, not sufficientlly practical. One more problem is that
three algorithms are all hierarchical. Non-hierarchical algorithms such as the k-means and iso data method are not
included in SAS cluster system.
The result by Ward method is shown in Fig.2 (a). As
known from Fig.2 (a)"",(c) , this classification is most accurate among three algorithms. Eight categories classified
in the procedure are water, river and shallows, grass, wood,
bare soil, residential, commercial, and asphalted area. Water area contains the sea and a pond with salt water. Wood
occupies verdart parks. Bare soil contains playgrounds of
school and open area being developed. Asphalted area contains roads, yards, and squares. Although these area are
comparatively accurate, residential area contains unclassified area partly.
REREFERENCES
Goldberg, S.W., and Shilien, S., 1978. A clustering scheme
for multidimensional images. IEEE Transaction on system,
man, and cybernetics, SMC-8(2):,86-92~
Joyner, S.P., 1985. The SAS User's Guide: Stasistics, Version 5 Edition, SAS Institute Inc.
3.3 average linkage
Koontz, W.L.G., Narendra, P., and Fukunaga, K., 1976. A
graph-theoretic approach to nonparametric cluster analysis.
IEEE Transaction on comp:uters, C-25(9):936-944.
The result by average linkage is shown in Fig.2 (b). The
classification in land area is incorrect. The main land cover
gives commercial, residential, grass, and wood, which are
joined to one cluster. Only bare soil is comparatively correct. Bare soil 1",,4 are essentially the same category. However, these bare soil 1",,4 have been separated due to the
characteristics of this algorithm.
Wharton, S.W., 1983. A generalized histogram clustering
scheme for multidimensional image data. Pattern Recognition, 16(2):193-199.
3.4 centroid method
197
Water
River and Shallows
16.58 %
5.67 %
Asphalted
17.83 %
Commercial
23.06 %
Residential
16.02 %
Bare soil
4.69 %
Grass
12.77 %
Wood
3.38 %
Water
20.40 %
Land
72.58 %
Grass
0.13 %
Bare soil 1
4.45
Bare soil 2
0.97 %
Bare soil 3
0.24 %
Bare soil 4
0.17 %
Crossroads
1.06 %
(a) Ward method
-
%
(b) average linkage
-
Water
18.32 %
Land
78.26 %
Grass
0.02 %
Bare soil 1
2.96 %
Bare soil 2
0.24-%
Bare soil 3
0.03 %
Bare soil 4
0.14 %
Crossroads
0.03 %
(c) centroid method
Fig.2. Results of cluster analysis of Fig.1 by three algorithms, which
show classification maps, categories, and rates of occupation.
198